The invention is directed to fuel supply lines as described hereinafter. Fuel supply are known, the walls of which are rigid and in which pressure dampers having elastic membranes are disposed in order to damp the pulsations of the fuel caused by the fuel supply pump and the intermittent action of the injection valves, as well as to avoid the transfer of annoying sounds to the vehicle body. To install a pressure damper in the fuel supply line does not only entail additional installation steps and causes space problems, but it also means additional costs.